The perimeter of a semicircle is 25.7 kilometers. What is the semicircle's diameter?

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Answer 1 · 2018-02-18T07:45:30

Diameter of the semicircle = 10 km.

perimeter of semicircle = $1/2$ the circumference + diameter

Given: perimeter of semicircle = $25.7 km$

Circumference of circle with radius $r$ = $2 pi r$ where $2r$ = diameter

$=> 25.7 = 1/2 xx 2 pi r + 2r$

$=> 25.7 = pi r +2r = r ( pi +2)$

$=> 25.7 = r( 3.14 +2 )= r(5.14)$

$=> r = 25.7 / 5.14 = 5$

$therefore radius = 5 km$

$=> diameter = 2r = 10 km$